Recent Glacier Retreat Exceeds Internal Variability...1NOVEMBER 2002 REICHERT ET AL. 3071 FIG.2. Glacier-speciﬁc SSC for (a) Nigardsbreen and (b) Rhonegletscher (Reichert et al

1 NOVEMBER 2002 3069R E I C H E R T E T A L .

q 2002 American Meteorological Society

Recent Glacier Retreat Exceeds Internal Variability

B. K. REICHERT* AND L. BENGTSSON

Max Planck Institute for Meteorology, Hamburg, Germany

J. OERLEMANS

Institute for Marine and Atmospheric Research Utrecht, Utrecht, Netherlands

(Manuscript received 27 August 2001, in final form 4 April 2002)

ABSTRACT

Glacier fluctuations exclusively due to internal variations in the climate system are simulated using downscaledintegrations of the ECHAM4/OPYC coupled general circulation model (GCM). A process-based modeling ap-proach using a mass balance model of intermediate complexity and a dynamic ice flow model considering simpleshearing flow and sliding are applied. Multimillennia records of glacier length fluctuations for Nigardsbreen(Norway) and Rhonegletscher (Switzerland) are simulated using autoregressive processes determined by statis-tically downscaled GCM experiments. Return periods and probabilities of specific glacier length changes usingGCM integrations excluding external forcings such as solar irradiation changes, volcanic, or anthropogeniceffects are analyzed and compared to historical glacier length records. Preindustrial fluctuations of the glaciersas far as observed or reconstructed, including their advance during the ‘‘Little Ice Age,’’ can be explained byinternal variability in the climate system as represented by a GCM. However, fluctuations comparable to thepresent-day glacier retreat exceed any variation simulated by the GCM control experiments and must be causedby external forcing, with anthropogenic forcing being a likely candidate.

1. Introduction

Quantifying natural climate variability and under-standing the underlying physical mechanisms are majorscientific goals of current climate research, also withrespect to the investigation of anthropogenic impacts onclimate. Examples for preindustrial climatic variationsover the past millennium are climate epochs in Europeand neighboring regions with predominantly cold pe-riods during roughly the seventeenth–nineteenth andwarm periods during the eleventh–fourteenth centuries,often referred to as the ‘‘Little Ice Age’’ and the ‘‘Me-dieval Warm Period’’ (Lamb 1977; Grove 1988), re-spectively, although the timing of these periods for dif-ferent regions of the globe has been questioned anddemonstrated to vary considerably (Bradley and Jones1993; Hughes and Diaz 1994; Folland et al. 2001, theirsection 2.3).

What are the possible physical processes responsiblefor preindustrial climatic variations over the past mil-

* Current affiliation: Lamont-Doherty Earth Observatory, Colum-bia University, Palisades, New York.

Corresponding author address: Dr. Bernhard K. Reichert, Lamont-Doherty Earth Observatory, Columbia University, 61 Route 9W, Pal-isades, NY 10964.E-mail: [email protected]

lennium lasting for decades or centuries? Volcanic ac-tivity affects the global climate (Hansen et al. 1992;Lindzen and Giannitsis 1998), but only a series of majoreruptions is likely to cool global temperature on decadalor longer timescales. Estimations of variability in solarirradiation (Lean et al. 1995; Hoyt and Schatten 1993)are based on indirect and fragmentary evidence but mayexplain global temperature changes at a level of a fewtenths of a degree (Cubasch et al. 1997). However, itappears that a dominant part of climatic variability overthe past millennium may be explained by internal var-iability in the climate system. Hasselmann (1976) dem-onstrated that low-frequency variations in a system suchas the climate could simply be the integrated responseof a linear (or nonlinear) system forced by short-termvariations resulting, for example, from the macrotur-bulent atmospheric flow at midlatitudes. The dynamicsof a physical system can turn short-term stochastic forc-ing into low-frequency climate variability. This has beendemonstrated using ocean general circulation models(Mikolajewicz and Maier-Reimer 1990) and is also ap-plicable to the dynamic response of glacier systems (Pat-erson 1994) as investigated in this study. Other possiblemechanisms inherent to the climate system are internalocean variability, ENSO variability, and other coupledatmosphere–ocean modes (Sarachik et al. 1996; Bengts-son and Reichert 2000; Bengtsson 2001).

3070 VOLUME 15J O U R N A L O F C L I M A T E

FIG. 1. Process-based modeling approach for the simulation ofglacier fluctuations applied in this study. Statistically downscaledGCM integrations are used for mass balance calculations using gla-cier-specific seasonal sensitivity characteristics (SSCs) based on amass balance model. Glacier length records are simulated using adynamic ice flow model and can finally be compared to observed orreconstructed historical glacier fluctuations.

General circulation models (GCMs) integrated overlong periods of time are essential tools in investigatingthe role of forcing factors. As an example, we inves-tigate in this study to what extent fluctuations of specificglaciers in Europe (observed or reconstructed both priorto industrialization and within the twentieth century) canbe explained by internal climate variations as simulatedby a coupled GCM. External forcings such as solar ir-radiation changes, volcanic, or anthropogenic effects areexcluded in the GCM experiments.

Glacier fluctuations result from changes in the massand energy balance at the earth’s surface and representvaluable paleoclimatic proxy data providing importantinformation on climate variability over long periods oftime. They are also key elements for the early detectionof climate change and possible anthropogenic impactson climate. Changes in glacier mass balance are definedas the annual mass gain or loss at the surface of a glacier(Paterson 1994). They can be viewed as the direct re-action of a glacier to climatic variations without delay.The mean specific mass balance of a glacier is the massbalance over the entire glacier surface. Mass balancevariations are mainly sensitive to the seasonal distri-butions of both temperature and precipitation, with sen-sitivities varying enormously among individual glaciers.For example, for the maritime glacier Nigardsbreen(Norway), it has been shown (Reichert et al. 2001) thata 18C higher temperature in summer [June–July–August(JJA)] can have the same effect on mean specific massbalance as 20% less precipitation in winter [December–January–February (DJF)]. The process-based modelingapproach applied in this study (Fig. 1) accounts for thesestrongly varying seasonally dependent sensitivity char-acteristics for individual glaciers (section 2).

Variations in glacier length are the indirect, delayed,filtered, and strongly enhanced response to climatic var-iations and are, therefore, much more difficult to inter-pret than glacier mass balance. However, the availablerecords of observed or reconstructed historic glacierlength fluctuations are much longer (often multicenten-nial) than available mass balance records (usually lessthan 50 yr). In order to be able to compare these longglacier length records to modeling studies, a dynamicice flow model calculating the response of glacier ge-ometry (including the position of the glacier front) tochanges in specific mass balance is used in this study(section 3). We simulate specific glacier length fluctu-ations for the temperate valley glaciers Nigardsbreen(Norway; 618439N, 78089E) and Rhonegletscher (SwissAlps; 468379N, 88249E) for comparison with historicalrecords of glacier length (section 5). In order to simulatelong, statistically significant records of low-frequencyglacier length fluctuations, we introduce a method usingautoregressive processes to generate multimillennia re-cords of mass balance from temporally limited GCMintegrations (section 4). We investigate the probabilitythat preindustrial glacier length variations can be ex-plained by internal fluctuations inherent to the climate

and the glacier system. We furthermore examine wheth-er it is likely that the general retreat of the glaciersobserved during the twentieth century, may be ex-plained by internal variations as simulated by a GCMor whether additional external forcing, such as anthro-pogenic forcing, is required (sections 6 and 7).

2. GCM experiments and simulation of massbalance

We use statistically downscaled integrations of thecoupled general circulation model ECHAM4/OPYC(Roeckner et al. 1996, 1999) thereby extending studiesassuming purely white-noise climatic forcing (Oerle-mans 2000, 2001). The atmospheric model ECHAM4has 19 levels in the vertical extending up to 10 hPa. Itis coupled to the full ocean general circulation modelOPYC (Oberhuber 1993) consisting of three submodelsfor the interior ocean, for the surface mixed layer, andfor sea ice (dynamic–thermodynamic sea ice model in-cluding viscous plastic rheology). The control integra-tion used in this study has been integrated at T42 res-olution (corresponding to a latitude–longitude grid ofabout 2.88 3 2.88) excluding any external forcing such


FIG. 2. Glacier-specific SSC for (a) Nigardsbreen and (b) Rhonegletscher (Reichert et al. 2001). The SSC representsthe dependence of glacier mass balance on monthly perturbations in temperature [solid bars; unit: mwe K 21, wheremwe means meter water equivalent] and precipitation [shaded bars; unit: mwe (10%) 21].

as solar irradiation changes, volcanic, or anthropogeniceffects. The concentrations of carbon dioxide, methane,and nitrous oxide are fixed at the observed 1990 values(Houghton et al. 1990, their Table 2.5). After a 100-yrspinup, the model has been integrated with constant fluxadjustment for 300 yr (Roeckner et al. 1999). Statisticaldownscaling of GCM integrations is based on daily re-analyses of the European Centre for Medium-RangeWeather Forecasts (ECMWF; Gibson et al. 1997) andweather station data in the vicinity of the investigatedglaciers, a detailed description of the method can befound in Reichert et al. (1999).

A process-based modeling approach using a mass bal-ance model of intermediate complexity (Oerlemans1992) and glacier-specific seasonal sensitivity charac-teristics (SSCs; Oerlemans and Reichert 2000) is appliedin order to simulate glacier mass balance for Nigards-breen and Rhonegletscher. The SSCs represent the de-pendence of the mean specific mass balance on monthlyperturbations in temperature and precipitation and havebeen calculated from the process-based mass balancemodel, individually for each glacier.

The SSCs for Nigardsbreen and Rhonegletscher areshown in Fig. 2. For the maritime glacier Nigardsbreen(Fig. 2a), the melt season especially on the lower partsof the glacier is long, the sensitivity to changes in tem-perature is high from May to October. Temperatureanomalies during these months lead to a strong responsein mass balance whereas temperature changes in winter(DJF) have almost no effect since melting hardly occurs.The sensitivity of mass balance to relative changes inprecipitation is very low in summer (JJA) since summerprecipitation falls as rain over most parts of the glacier.In winter, precipitation mainly falls as snow and can beadded to the surface, naturally leading to a strong effecton the annual mass balance.

Since the accumulation area of Rhonegletscher (Fig.2b) is located at higher altitudes (2140–3620 m) com-

pared to Nigardsbreen (295–1950 m), lower annual airtemperatures at the equilibrium line of the glacier (char-acterizing the glacier in its climatic and topographicsetting) lead to a considerable effect also of summerprecipitation (with a large fraction falling as snow atthese altitudes). The sensitivity is in fact almost constantover the entire year. With respect to changes in monthlytemperature, Rhonegletscher is generally less sensitivethan Nigardsbreen.

Further details on the mass balance model, individualsimulations using the SSCs, model validation usingECMWF reanalyses, and the impact of the North At-lantic Oscillation (NAO) on mass balance fluctuationsof Nigardsbreen and Rhonegletscher are provided inReichert et al. (2001). The study revealed a high cor-relation between decadal variations in the NAO andmass balance, with winter precipitation associated withthe NAO being the dominant factor. A high NAO phasemeans enhanced (reduced) winter precipitation for Ni-gardsbreen (Rhonegletscher), typically leading to ahigher (lower) than normal annual mass balance. It hasbeen found that this mechanism can also explain ob-served strong positive mass balances for Nigardsbreenand other maritime Norwegian glaciers within the pe-riod 1980–95.

3. The ice flow model

In order to be able to use long records of historicglacier fluctuations for comparison with model experi-ments, a dynamic ice flow model is needed. It calculatesthe response of glacier geometry to changes in specificmass balance. Cumulative glacier mass changes lead tochanges in ice thickness that then influence the dynamicredistribution of mass by glacier flow (Haeberli 1995).In the following, a brief description of the ice flowmodel used in this study (Oerlemans 1997) is presented.

The prognostic equation of the ice flow model is a


continuity equation describing conservation of ice vol-ume:

]S ](US)5 2 1 vB.

]t ]x

Here, x is the coordinate along the flowline of theglacier, U is the vertical mean ice velocity, S is the areaof a cross section through the glacier perpendicular tothe flowline (parameterized by a trapezoidal cross sec-tion), B is the mass balance, and v is the glacier widthat the surface.

Both simple shearing flow and sliding are consideredin the model. The vertical mean ice velocity U is de-termined by the local ‘‘driving stress’’ t that is pro-portional to ice thickness H and surface slope ]h/]x (his surface elevation). After rearrangement of equations(Oerlemans 1997) it follows that ice thickness H is gov-erned by a nonlinear diffusion equation that has to besolved by the ice flow model:

]H 21 ] ](b 1 H )5 D 1 B.[ ]]t v 1 lH ]x ]x0

Here, H is the ice thickness, and b and v0 are theelevation and the width of the bed of the glacier, re-spectively. The l is determined by (v 2 v0)/H. Thediffusivity D can be expressed as

2 2l ]h ]h

5 3D 5 v 1 H f gH 1 f gH ,0 d s1 2 1 2 1 2[ ]2 ]x ]x

with h as surface elevation, f d and f s as generalizedviscosities referring to deformation and sliding, respec-tively, and g determined by (rg)3 with ice density r andacceleration due to gravity g.

The equations are solved using standard numericalmethods for parabolic equations. Ice thickness, ice ve-locity, ice volume, and glacier length L are obtained.

If a climatic state is changed stepwise from a statewith equilibrium glacier length L1 to a state with equi-librium glacier length L2, the (e folding) response timefor glacier length trL is defined as the time the glacierneeds to reach glacier length L2 2 (L2 2 L1)/e. Usingthe above model, the response time of Nigardsbreen toa stepwise change in the annual mass balance (dB 560.4 m water equivalent; Oerlemans 1997) is 68 yr, forRhonegletscher it is 61 yr.

4. Autoregressive processes for the simulation ofmass balance using GCMs

In order to be able to quantify natural variations inglacier length with high statistical significance, long re-cords of mass balance are required to force the dynamicice flow model. Due to the long response times of theinvestigated glaciers (60–70 yr, see the previous section)mass balance time series in the order of thousands ofyears would be most suitable. However, the output of

current coupled GCMs is naturally limited owing to highcomputational costs. For example, the ECHAM4/OPYCcoupled GCM control integration used in this study hasbeen integrated for 300 yr.

Owing to these limitations, in this study, we apply amethod to generate multimillennia records of mass bal-ance from temporally limited GCM integrations usingautoregressive (AR) processes.

a. General method

An autoregressive process Xt of the order p, that is,an AR(p) process, is generally defined as

p

X 5 a 1 a X 1 Z ,Ot 0 k t2k tk51

where a0, a1, . . . , ap are constants (autoregressive pa-rameters), ap ± 0, and Zt is a white-noise process. Thename ‘‘autoregressive’’ indicates that the processevolves by regressing past values toward the mean (witha ‘‘strength’’ determined by the autoregressive param-eters ak and then adding noise (von Storch and Zwiers1999).

We fit an AR process to the mass balance time seriessimulated from GCM output and generate a new massbalance time series of the desired length with similarproperties. This involves 1) calculation of the autocor-relation function of the original time series, 2) fitting ofan AR model to the time series, that is, estimation ofthe autoregressive parameters ak (an iterative nonlinearleast squares procedure incorporating backforecasting isused; Box and Jenkins 1976), and 3) generation of anew time series with a similar autocorrelation functionand standard deviation as the original. This procedureis applied individually to the simulated mass balancerecords for Nigardsbreen and Rhonegletscher.

b. AR processes applied to Nigardsbreen andRhonegletscher

The spectra of glacier mass balance as simulated bythe GCM experiments (Reichert et al. 2001) are shownin Fig. 3. Thin solid lines denote the spectra of equiv-alent red-noise processes and dashed lines represent the95% confidence levels for accepting the red-noise nullhypothesis. We generate 10 000-yr records of mass bal-ance for the two glaciers with comparable frequencycharacteristics and similar standard deviations as theoriginal time series.

We find that the mass balance time series for Ni-gardsbreen simulated by the coupled GCM experimentcan be well approximated by a third-order AR process(lag-1, lag-2, and lag-3 autocorrelation coefficients are0.11, Table 1). Neither simply white noise nor red noisewould be appropriate for the representation of the low-frequency characteristics of the mass balance time se-ries. In fact, using a third-order AR process instead of


FIG. 3. Spectra of glacier mass balance records for (a) Nigardsbreen and (b) Rhonegletscher as simulated by thecoupled GCM experiment. Thin solid lines denote the spectra of equivalent red-noise processes and dashed linesrepresent the 95% confidence levels for accepting the red-noise null hypothesis.

TABLE 1. Autocorrelation coefficients of the original GCM andof the generated 10 000-yr mass balance records (in parentheses)using a third-order AR process determined by the AR parameters a1,a2, and a3 estimated by the AR model.

Autocorrelation coefficients

Lag 1 Lag 2 Lag 3

Nigardsbreen 0.11 (0.12)a1 5 0.091

0.11 (0.12)a2 5 0.089

0.11 (0.11)a3 5 0.092

Rhonegletscher 0.04 (0.04)a1 5 0.044

0.003 (0.002)a2 5 20.004

0.004 (0.003)a3 5 0.010

a simple white-noise process increases the variability inglacier length fluctuations by 36% as will be demon-strated in section 5. For Rhonegletscher, this impact issmaller, the simulated spectrum of mass balance maybe approximated by a first-order AR process (lag-1 co-efficient: 0.04; lag-2 and lag-3 coefficients: ,0.01). Wecan expect a small impact on low-frequency glacierlength fluctuations as will be seen in section 5.

Table 1 shows the autoregressive parameters a1, a2,and a3 as estimated by the AR model using the iterativenonlinear least squares procedure. A higher than third-order AR process is not required; we find that it doesnot significantly improve the fit of the model any further.The differences between the autocorrelation coefficientsof the original and the generated mass balance records(Table 1; shown in parentheses) are small and not sig-nificant for the purpose of the present study.

5. Simulation of glacier length fluctuations

The 10 000-yr mass balance records using AR pro-cesses obtained from the coupled GCM are used to forcethe dynamic ice flow model for Nigardsbreen and Rho-negletscher. Again, it should be emphasized that thesimulated glacier length records are exclusively due to

internal variations in the climate and glacier systemsince external forcing has been excluded in the GCMintegration. We have simulated three individual 10 000-yr glacier length records for each glacier in order toinvestigate the following:

1) the impact of using the AR process determined byGCM output instead of simply using white noise,and

2) the influence of using the statistically downscaledGCM integrations instead of simply interpolatingcoarse GCM gridpoint output to the location of theglaciers.

The results are presented in Fig. 4. Note that the timeaxes of the simulated records are not related to actualcalendar years; we are solely interested in the possiblerange of internal glacier fluctuations. To facilitate thecomparison with observations in the following section,the glacier model has been initialized to simulate var-iations around a mean level of observed preindustrialglacier lengths. The first glacier length record in eachexperiment [marked as ‘‘White Noise (Not Down-scaled)’’ in the left part of each graph in Fig. 4] issimulated simply by using Gaussian white noise as massbalance forcing, with a standard deviation obtained fromdirectly interpolated GCM gridpoint output without sta-tistical downscaling. This means that the record repre-sents glacier fluctuations that could be expected if nei-ther the spectral characteristics of GCM output nordownscaling played any role. The second record in eachexperiment [marked as ‘‘AR Process (Not Down-scaled)’’] shows the impact of using a third-order ARprocess accounting for the spectral characteristics of theGCM integrations. The standard deviations of the massbalance forcing records are similar to the first record,statistical downscaling is not applied. The third record


FIG. 4. The 10 000-yr records of simulated glacier length fluctuations for (a) Nigardsbreen and (b) Rhonegletscher. The figure demonstratesthe impact of using AR processes determined by GCM output as mass balance forcing (middle record) instead of simply using white noisewith the same variance (left-hand records), and the impact of statistical downscaling (right-hand records). Std devs s of glacier length areshown below each record.

[‘‘AR Process (Downscaled)’’] additionally considersthe impact of statistical downscaling and is thereforeconsidered as the most comprehensive representation ofglacier fluctuations simulated in this study.

The standard deviations s of glacier length fluctua-tions for each experiment are shown below each record.For Nigardsbreen, using a third-order AR process de-termined from the coupled GCM experiment instead ofa white-noise process (Fig. 4a) increases the variabilityin glacier fluctuations by 36% (standard deviations in-crease from 0.36 to 0.49 km). As mentioned above, thisemphasizes the high impact of the AR process for thegeneration of low-frequency glacier fluctuations. Sta-tistical downscaling additionally increases the variabil-ity by another 12% (from 0.49 to 0.55 km).

As could be expected from the almost white massbalance spectra of Rhonegletscher (Fig. 3b), the influ-ence of the AR process on glacier length variations forthis glacier is only marginal (Fig. 4b). However, due tothe local setting of this glacier, the impact of down-scaling is high, glacier length variability is increased byabout 50% (from 0.19 to 0.29 km; Fig. 4b). This showsthe substantial influence of statistical downscaling inthis region of the Alps (Reichert et al. 2001). With re-spect to local observational data, the direct coarse grid-point output of a GCM would have considerably un-

derestimated the local climatic variability responsiblefor the length fluctuations of this glacier.

6. Comparison with observed glacier lengthfluctuations and statistical analysis

Simulated glacier fluctuations are compared to ob-served historical glacier length records for Nigardsbreenand Rhonegletscher. Assuming that the occurrence ofglacier fluctuations generally follows a Poisson process(events occur independently at random instants of timeand at a constant mean rate per time interval; Priestley1981), we investigate the probabilities of preindustrialglacier fluctuations on one hand and the present-dayretreat of the glaciers on the other hand to be explainedby internal variations in the climate system as simulatedby the GCM.

a. Historical records of glacier length changes

Observed or reconstructed glacier length variationsfor the two glaciers are shown in Fig. 5. Various historicdocuments, terminal moraines, photogrammetric meth-ods, and distance measurements have been combined toobtain this record (Hoelzle and Haeberli 1999).

During the first half of the eighteenth century, Ni-


FIG. 5. Observed or reconstructed historical glacier length varia-tions for Nigardsbreen (solid line; diamonds are data points) andRhonegletscher (dotted line; circles are data points). Data from Hoel-zle and Haeberli (1999).

gardsbreen advanced rapidly (the time of the beginningof the advance is uncertain) and reached a neoglacialmaximum in 1748. Since then, a retreat has been ob-served until about 1990, which thereafter, came to anend. The retreat of the glacier until 1900 (in the fol-lowing noted as ‘‘Little Ice Age to 1900 retreat’’) isabout 2 km for Nigardsbreen. The retreat until 1990(‘‘Little Ice Age to present-day retreat’’) is roughly 4km.

Rhonegletscher advanced at the beginning of the re-cords until 1602, followed by a period for which glacierlength remained within a range of 11.6–12.1 km until1860. This time then marks the beginning of a rapidretreat. The Little Ice Age to 1900 retreat of the glacier,considering its maximum in 1602, is roughly 1.5 km;the Little Ice Age to present-day retreat is about 2.3km.

b. Analysis of simulated glacier fluctuations

Figure 6 shows the first 2000 yr of the simulated10 000-yr glacier length records using AR processesincluding downscaling, along with the observationsfor Nigardsbreen (Fig. 6a) and Rhonegletscher (Fig.6b). As for Fig. 4, the time axes of the simulatedrecords are not related to actual calendar years, weare solely interested in the possible range of internalglacier fluctuations. The simulated records show sub-stantial changes in glacier length lasting for decadesor even several centuries. Nevertheless, it appears thatthe observed retreat of the glaciers since their LittleIce Age maximum exceeds any glacier fluctuation inthe corresponding simulated records using the cou-pled GCM. Fluctuations in the order of reconstructedvariations before 1900 do, however, occur in the sim-ulated records and may therefore be explainable byinternal climate variations as simulated by the GCM.

For a further analysis, recurrence relationships for spe-cific glacier length fluctuations are calculated. The distri-bution of glacier fluctuations for the complete 10 000-yrrecords is shown in Fig. 7. Glacier length changes arecalculated between a local extreme value and a subsequent‘‘significant’’ extreme value, which means that continuousglacier length changes are considered until a significantreversal of the movement of the glacier tongue occurs.Significant means that only glacier length changes withamplitudes larger than one-half of the simulated standarddeviation s (0.27 km for Nigardsbreen, 0.15 km for Rho-negletscher; Fig. 4) are considered to interrupt a continuinglarger advance or retreat of the glacier. This emphasizesour interest in larger, longtime fluctuations; small inter-ruptions within a movement (as, e.g., the observed smalladvance of Rhonegletscher at around year 1920; Fig. 5)do not affect the analysis. The velocity of the movementis not considered, slowdowns or standstills do not affectthe analysis until a significant reversal of the glacier move-ment is initiated. The maximum change in glacier lengthover the complete simulated 10 000-yr records is an ad-vance of 2.8 km for Nigardsbreen (Fig. 7a) lasting forabout 200 yr (Fig. 6a; at around model year 11200). ForRhonegletscher, the maximum change is a retreat of 1.3km (Fig. 7b) lasting for more than 100 yr (see Fig. 6b; ataround model year 11900). The corresponding recurrencerelationships are shown on a logarithmic scale in Fig. 8,the cumulative number of events N is plotted against gla-cier length changes DL. The relationships can be wellapproximated by exponential regression, the recurrencerelationships can be expressed as

logN 5 21.77DL 1 5.46 (Nigardsbreen) and

logN 5 22.96DL 1 5.45 (Rhonegletscher).

It may be noted that the largest simulated glacierlength fluctuations (DL . 2.5 km for Nigardsbreen andDL . 1.1 km for Rhonegletscher; Fig. 8) are not com-pletely in line with the regression. This can be expectedsince they occur only a few times within the 10 000-yrrecords thus representing a sampling problem.

c. Return periods of specific glacier length changes

On the basis of the above established recurrence re-lationships, we determine return periods a for the oc-currence of specific glacier fluctuations due to internalclimate variations as simulated using the coupled GCMintegrations:

T Tsim sim 2a 2bDLa(DL) 5 5 5 (T e )e .simbDL1aN(DL) e

Here, Tsim is the time period simulated (10 000 yr inour experiments), a and b are the glacier-specific re-gression parameters in the recurrence relationships (Ni-gardsbreen: a 5 5.46, b 5 21.77; Rhonegletscher: a5 5.45, b 5 22.96; see above).

Table 2 shows that glacier fluctuations of at least


FIG. 6. Observed and simulated glacier fluctuations for (a) Nigardsbreen and (b) Rhonegletscher. Simulated glacierlength fluctuations are exclusively due to internal variations in the climate system using AR processes from thedownscaled control integration of the ECHAM4/OPYC coupled GCM.

FIG. 7. Histogram of simulated glacier fluctuations using the downscaled coupled GCM integration. The cumulativenumber of events represents glacier length changes in the simulated 10 000-yr records with amplitudes larger thanthe value given on the abscissa (bin width: 0.2 km).


FIG. 8. Recurrence relationships showing the cumulative number of glacier fluctuation events N for a minimumglacier length change DL in the simulated 10 000-yr records. The relationships are well approximated by exponentialregression.

TABLE 2. Return periods for specific glacier length fluctuations.

Lengthchange

Nigardsbreen(yr)

Rhonegletscher(yr)

DL$0.5 kmDL$1.0 kmDL$1.5 kmDL$2.0 kmDL$2.5 kmDL$3.0 km

104252611

148235958725

189831

365016023

(;1 3 105)(;3 3 105)

FIG. 9. Graphical illustration of return period a (yr) for glacierlength changes larger than DL (in km) for Nigardsbreen (solid line)and Rhonegletscher (shaded line).

1 km can roughly be expected to occur every 250 yrfor Nigardsbreen and every 800 yr for Rhonegletscher.The observed Little Ice Age to 1900 retreat of 2 km forNigardsbreen can be expected with a return period ofabout 1500 yr exclusively due to internal climate fluc-tuations. For extreme glacier length fluctuations of 3 kmwe find return period of about 8700 yr. For Rhone-gletscher, the Little Ice Age to 1900 retreat of 1.5 kmis expected to occur every 3700 yr. An extreme changeof 2-km length has not been simulated for this glacierin the 10 000-yr record; however, in a longer integrationwe could expect it to occur with a return period of about16 000 yr. Figure 9 is a graphical illustration of returnperiods.

d. Probabilities for the simulation of observedpreindustrial glacier length changes and thepresent-day glacier retreat

Probabilities for specific glacier fluctuations within agiven time interval are calculated assuming that theiroccurrence generally follows a Poisson process (Priest-ley 1981). This approach also accounts for the fact thatextreme glacier length changes that may not have beensimulated in the 10 000-yr record still have a certain

(although small) statistical probability of occurrence andmay well occur in an even longer simulated record. Theprobability P for the occurrence of a glacier lengthchange DL (represented by its return period a) withina time interval T can be expressed as

2T/aP(T, a) 5 1 2 e .

Substituting return period a with the definition insection 6c, we may write

TbDL1aP(T, DL) 5 12 exp 2 e .1 2Tsim

Here Tsim is the length of simulated records, and aand b are the regression parameters obtained from therecurrence relationships.


FIG. 10. Probabilities P for the occurrence of simulated glacier length changes DL within a time periodof investigation T, exclusively due to internal climate variations as simulated using the ECHAM4/OPYCcoupled GCM. (a) For Nigardsbreen, the probability that observed preindustrial glacier length changes of2 km (Little Ice Age to 1900 retreat) occur within a time period of 10 000 yr is 99.8%, whereas the present-day retreat (4 km) is unlikely to be explained by internal variability (P 5 17.7%). (b) For Rhonegletscher,the probabilities are 93.5% and 22.6%, respectively.

The P(T, DL) relations for both Nigardsbreen andRhonegletscher are illustrated in Fig. 10. We show prob-abilities of occurrence P for glacier fluctuations DLwithin investigated time periods of T 5 100, T 5 500,T 5 2000, and T 5 10 000 yr.

For Nigardsbreen (Fig. 10a), the probability that ob-served preindustrial glacier length changes of 2 km (Lit-tle Ice Age to 1900 retreat, see Fig. 5) occur within atime period of 10 000 yr exclusively due to internalclimate variations is 99.8% (Fig. 10a, solid line), theseglacier fluctuations actually frequently occur in the sim-ulated record (see Fig. 7). On the other hand, the ob-served Little Ice Age to present-day retreat of 4 km (seeFig. 5) has not been simulated due to internal climatic

variability, the probability of occurrence is correspond-ingly small (17.7%). Looking at a time period of 2000yr only (Fig. 10a, shaded line), the probability of oc-currence for preindustrial glacier fluctuations is still74.1%, whereas the probability for the present-day re-treat drops to 3.8%.

For Rhonegletscher (Fig. 10b), the probability of pre-industrial glacier length changes within a 10 000-yr in-terval (solid line) is 93.5%, for the present-day retreatit is 22.6%. This means that the situation here is gen-erally comparable to Nigardsbreen, preindustrial fluc-tuations are likely to occur in the simulated recordswhereas the present-day retreat is not simulated by anyinternal variation as represented by the coupled GCM.


FIG. 11. Glacier length rates (unit: m yr21) for (a) Nigardsbreen and (b) Rhonegletscher calculated for200-yr windows (abscissa shows center value) (left) moving over the entire 10 000-yr time period ofsimulations and (right) over the observational time periods. The observed negative length rates for bothglaciers substantially exceed the simulated length rates for any 200-yr time period within the 10 000-yrrecords.

e. Rates of glacier length changes

Another perspective for the investigation of simulatedand observed glacier length changes with time can beprovided using rates of glacier length changes. Rates(unit: m yr21) of glacier advance/retreat for 200-yr timeperiods within both the 10 000-yr simulations and theobservational data are shown in Fig. 11. It is evidentthat the observed negative length rates for both glacierssubstantially exceed simulated length rates for any 200-yr time period within the 10 000-yr records. No glacierretreat has been simulated due to internal climate var-iability that shows the same negative length rates overa 200-yr time interval as the observed retreat. Thismeans that in addition to the total length changes of thepresent-day glacier retreat (as demonstrated above) wealso find exceptional rates of change within 200-yr pe-riods.

7. Summary and conclusions

In this study, we have applied a process-based mod-eling approach for the simulation of glacier fluctuationsexclusively due to internal variations in the climate sys-tem using a downscaled coupled GCM experiment with

ECHAM4/OPYC. A mass balance model of interme-diate complexity and a dynamic ice flow model havebeen used to simulate glacier fluctuations for Nigards-breen (Norway) and Rhonegletscher (Swiss Alps). Wehave shown that local downscaling has a considerableimpact on glacier fluctuations, the variability in glacierlength is substantially increased compared to simply us-ing direct coarse GCM gridpoint output. Simulated gla-cier fluctuations have been statistically analyzed in orderto compare them to observed or reconstructed historicalglacier length records. On the basis of recurrence re-lationships, return periods of specific glacier fluctuationevents have been determined.

The observed retreat of Nigardsbreen since its ‘‘LittleIce Age maximum’’ until 1900, can be expected to occurroughly every 1500 yr exclusively due to internal cli-mate fluctuations as simulated by the coupled GCMexperiment. For Rhonegletscher, such a retreat can beexpected with a return period of about 3700 yr due tointernal variability. Calculations of probabilities con-sequently indicate that for both glaciers, fluctuations asobserved or reconstructed before 1900 are simulated tooccur in all likelihood due to internal climate variability.On the other hand, the observed present-day retreat of


the glaciers has not been simulated in the experimentsand is therefore very unlikely to be explainable by in-ternal variations in the climate system.

We conclude that fluctuations of the investigated gla-ciers as far as observed or reconstructed before 1900,including their advance during the ‘‘Little Ice Age,’’can be explained by internal variations in the climatesystem as simulated by a GCM. This does not meanthat other climatic forcing factors, for example, volcanicactivity or solar irradiation changes may not partly con-tribute to explain observed glacier fluctuations. The im-pact of these factors, relative to internal climate vari-ability, will increase with larger (up to hemispheric/global) spatial scales. We show, however, that internalclimate variations have a dominant impact when inter-preting dynamic glacier records on at least regionalscales. In order to broaden the basis for our conclusionswe have additionally performed similar experiments us-ing control integrations of the ECHAM4 model coupledto a mixed layer ocean model (ECHAM4/MLO; Roeck-ner 1997) and the second Hadley Centre CoupledOcean–Atmosphere General Circulation Model(HadCM2; Johns et al. 1997) with results similar asdescribed above (not shown). The impact of forced nat-ural climate variability will be further investigated infuture experiments using externally forced GCM inte-grations, also with recent studies in mind (Shindell etal. 2001) suggesting a potential impact of solar forcingon the European climate as a consequence of changesin the Arctic Oscillation/North Atlantic Oscillation (AO/NAO).

An important point of this study derives from the factthat the present-day glacier retreat exceeds any simu-lated glacier fluctuation using the GCM control inte-grations. We have shown that it is consequently unlikelythat this retreat can be entirely caused by internal climatevariability and that external forcing must be a contrib-uting factor. In additional experiments, we have inves-tigated the role of anthropogenic forcing as a potentialcandidate. The process-based approach developed inthis study has been applied to transient integrations withECHAM4/OPYC forced by increasing concentrations ofgreenhouse gases, sulphate aerosols, and troposphericozone over the period 1860–2050 (Roeckner et al.1999). In spite of a considerable impact of internal var-iations superimposed on the general trend over this pe-riod, first results for Nigardsbreen indicate that the ob-served present-day retreat is comparable to the simu-lated retreat expected due to anthropogenic forcing. Theexperiments therefore suggest that climate change dueto anthropogenic forcing is a likely explanation for theobserved glacier retreat. The transient GCM experi-ments predict a considerable future retreat of Nigards-breen due to anthropogenic forcing, they indicate a re-treat of about 20% of the present-day glacier length(10.3 km) by 2050. Details of these experiments willbe investigated in an additional study.

This study is spatially limited to the investigated gla-

cier sites and only future experiments using a large num-ber of globally distributed glaciers will allow conclu-sions on a global scale. However, our results are in linewith recent studies (Haeberli et al. 1999; Dyurgerov andMeier 2000) indicating that rates and acceleration trendsof global glacier mass changes over at least the pastfour decades correspond to the overall effects of an-thropogenic forcing.

Acknowledgments. The authors would like to thankE. Roeckner, H. Graßl, D. Dommenget, J. Jones, andA. Tompkins for their valuable scientific support. Hansvon Storch is thanked for help concerning several sta-tistical issues within this study. We thank N. Noreiksfor help on graphic representation. Glacier mass balanceand glacier length data were obtained from the WorldGlacier Monitoring Service (WGMS), the ECMWF pro-vided meteorological reanalyses, and the Swedish Me-teorological and Hydrological Institute (SMHI) contrib-uted operational weather station data. The study wassupported by the European Commission under ContractENV4-CT95-0072 and by NOAA Grant NA165P1616.The Alexander von Humboldt Foundation is thankedfor supporting B. K. Reichert as a Feodor Lynen Fellow.Model simulations were performed at the German Cli-mate Computing Center (DKRZ) in Hamburg, Germany.

REFERENCES

Bengtsson, L., 2001: Uncertainties of global climate prediction. Proc.Symp. on Global Biogeochemical Cycles in the Climate System,Jena, Germany, Max Planck Institute for Biogeochemistry, 15–29.

——, and B. K. Reichert, 2000: Global climate change and naturalclimate variability—What are their reasons? (in German). Ener-gie und Umwelt—Wo Liegen Optimale Losungen? J. Wolfrumand S. Wittig, Eds., Union der deutschen Akademien der Wis-senschaften und Heidelberger Akademie der Wissenschaften,Springer Verlag, 27–57.

Box, G. E. P., and G. M. Jenkins, 1976: Time Series Analysis: Fore-casting and Control. Holden-Day, 575 pp.

Bradley, R. S., and P. D. Jones, 1993: ‘‘Little Ice Age’’ summertemperature variations: Their nature and relevance to recentglobal warming trends. Holocene, 3, 367–376.

Cubasch, U. R., R. Voss, G. C. Hegerl, J. Waszkewitz, and T. J.Crowley, 1997: Simulation of the influence of solar radiationvariations on the global climate with an ocean–atmosphere gen-eral circulation model. Climate Dyn., 13, 757–767.

Dyurgerov, M. B., and M. F. Meier, 2000: Twentieth century climatechange: Evidence from small glaciers. Proc. Natl. Acad. Sci.USA, 97, 1406–1411.

Folland, C. K., and Coauthors, 2001: Observed climate variabilityand change. Climate Change 2001: The Scientific Basis, J. T.Houghton et al., Eds., Cambridge University Press, 99–181.

Gibson, J. K., P. Kallberg, S. Uppala, A. Nomura, A. Hernandez, andE. Serrano, 1997: ERA description. ECMWF Re-Analysis Pro-ject Report Series, Rep. 1 ECMWF, Reading, United Kingdom,71 pp.

Grove, J. M., 1988: The Little Ice Age. Methuen, 498 pp.Haeberli, W., 1995: Glacier fluctuations and climate change detection.

Geogr. Fis. Dinam. Quat., 18, 191–199.——, R. Frauenfelder, M. Hoelzle, and M. Maisch, 1999: On rates

and acceleration trends of global glacier mass changes. Geogr.Annal., 81, 585–591.


Hansen, J., I. Fung, R. Ruedy, and M. Sato, 1992: Potential climateimpact of Mount Pinatubo eruption. Geophys. Res. Lett., 19,215–218.

Hasselmann, K., 1976: Stochastic climate models I: Theory. Tellus,28, 473–485.

Hoelzle, M., and W. Haeberli, 1999: World glacier monitoring service,world glacier inventory. National Snow and Ice Data Center,University of Colorado, Boulder, CO. [Available by e-mail re-quest to [email protected]]

Houghton, J. T., G. J. Jenkins, and J. J. Ephraums, Eds.,1990: ClimateChange: The IPCC Scientific Assessment. Cambridge UniversityPress, 364 pp.

Hoyt, D. V., and K. H. Schatten, 1993: A discussion of plausiblesolar irradiance variations 1700–1992. J. Geophys. Res., 98, 18895–18 906.

Hughes, M. K., and H. F. Diaz, 1994: Was there a ‘‘Medieval WarmPeriod’’ and if so where and when? Climatic Change, 26, 109–142.

Johns, T. C., R. E. Carnell, J. F. Crossley, J. M. Gregory, J. F. B.Mitchell, C. A. Senior, S. F. B. Tett, and R. A. Wood, 1997: TheSecond Hadley Centre coupled ocean–atmosphere GCM: Modeldescription, spinup and validation. Climate Dyn., 13, 103–134.

Lamb, H. H., 1977: Climatic History and the Future. Vol. 2, Climate:Present, Past and Future, Methuen, 835 pp.

Lean, J., J. Beer, and R. S. Bradley, 1995: Reconstruction of solarirradiance since 1610: Implications for climate change. Geophys.Res. Lett., 22, 3195–3198.

Lindzen, R. S., and C. Giannitsis, 1998: On the climatic implicationsof volcanic cooling. J. Geophys. Res., 103, 5929–5941.

Mikolajewicz, U., and E. Maier-Reimer, 1990: Internal secular var-iability in an ocean general circulation model. Climate Dyn., 4,145–156.

Oberhuber, J. M., 1993: Simulation of the Atlantic circulation witha coupled sea ice–mixed layer–isopycnal general circulationmodel. Part I: Model description. J. Phys. Oceanogr., 23, 808–829.

Oerlemans, J., 1992: Climate sensitivity of glaciers in southern Nor-way: Application of an energy-balance model to Nigardsbreen,Helstugubreen, and Alfotbreen. J. Glaciol., 38, 223–232.

——, 1997: A flow-line model for Nigardsbreen: Projection of future

glacier length based on dynamic calibration with the historicrecord. Ann. Glaciol., 24, 382–389.

——, 2000: Holocene glacier fluctuations: Is the current rate of retreatexceptional? Ann. Glaciol., 31, 39–44.

——, 2001: Glaciers and Climate Change. Balkema Publishers, 148pp.

——, and B. K. Reichert, 2000: Relating glacier mass balance tometeorological data using a seasonal sensitivity characteristic(SSC). J. Glaciol., 46, 1–6.

Paterson, W. S. B., 1994: The Physics of Glaciers. 3d ed. Pergamon,480 pp.

Priestley, M. B., 1981: Spectral Analysis and Time Series. AcademicPress, 890 pp.

Reichert, B. K., L. Bengtsson, and O. Akesson, 1999: A statisticalmodeling approach for the simulation of local paleoclimaticproxy records using general circulation model output. J. Geo-phys. Res., 104, 19 071–19 083.

——, ——, and J. Oerlemans, 2001: Midlatitude forcing mechanismsfor glacier mass balance investigated using general circulationmodels. J. Climate, 14, 3767–3784.

Roeckner, E., 1997: Climate sensitivity experiments with the MPI/ECHAM4 model coupled to a slab ocean (abstract). EuroclivarWorkshop on Cloud Feedbacks and Climate Change, C. A. Se-nior and J. F. B. Mitchell, Eds., Hadley Centre for Climate Pre-diction and Research, 20.

——, and Coauthors, 1996: The atmospheric general circulation mod-el ECHAM-4: Model description and simulation of present-dayclimate. Max Planck Institute for Meteorology Rep. 218, Ham-burg, Germany, 90 pp.

——, L. Bengtsson, J. Feichter, J. Lelieveld, and H. Rodhe, 1999:Transient climate change simulations with a coupled atmo-sphere–ocean GCM including the tropospheric sulfur cycle. J.Climate, 12, 3004–3032.

Sarachik, E. S., M. Winton, and F. L. Yin, 1996: Mechanisms fordecadal-to-centennial climate variability. Decadal Climate Var-iability, D. L. T. Anderson and J. Willebrand, Eds., NATO ASISeries, Vol. 44, Springer, 157–210.

Shindell, D. T., G. A. Schmidt, M. E. Mann, D. Rind, and A. Waple,2001: Solar forcing of regional climate change during the Maun-der Minimum. Science, 294, 2149–2152.

von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in ClimateResearch. Cambridge University Press, 484 pp.

Documents

Recent Glacier Retreat Exceeds Internal Variability...1NOVEMBER 2002 REICHERT ET AL. 3071 FIG.2. Glacier-speciﬁc SSC for (a) Nigardsbreen and (b) Rhonegletscher (Reichert et al